So I recently recieved a radeon 5670 from my neighbor and I was wondering if I'd be able to put into my computer that currently has a 6970 and if both of them would work. Both Cards are by XFX
Assuming that you're using this machine for gaming (compute apps are a bit different), there's no benefit to be had by adding an additional graphics card that isn't the same model as the existing card. The 5670 is a very weak card compared to the 6970.
The 6970 should be able to run up to 4 monitors just fine. If you need more than that, then sure the 5670 would work. It wouldn't add any performance if that's what you are asking.